hydraulics_supplyfunctions {medfate}

Hydraulic supply functions

Description

Set of functions used in the implementation of hydraulic supply functions (Sperry and Love 2015).

Usage

hydraulics_EXylem(
  psiPlant,
  psiUpstream,
  kxylemmax,
  c,
  d,
  allowNegativeFlux = TRUE,
  psiCav = 0
)

hydraulics_E2psiXylem(E, psiUpstream, kxylemmax, c, d, psiCav = 0)

hydraulics_E2psiXylemUp(E, psiDownstream, kxylemmax, c, d, psiCav = 0)

hydraulics_EVanGenuchten(psiRhizo, psiSoil, krhizomax, n, alpha, l = 0.5)

hydraulics_ECrit(psiUpstream, kxylemmax, c, d, pCrit = 0.001)

hydraulics_ECapacitance(
  psi,
  psiPrev,
  PLCprev,
  V,
  fapo,
  c,
  d,
  pi0,
  eps,
  timestep
)

hydraulics_E2psiVanGenuchten(
  E,
  psiSoil,
  krhizomax,
  n,
  alpha,
  psiStep = -1e-04,
  psiMax = -10
)

hydraulics_E2psiTwoElements(
  E,
  psiSoil,
  krhizomax,
  kxylemmax,
  n,
  alpha,
  c,
  d,
  psiCav = 0,
  psiStep = -1e-04,
  psiMax = -10
)

hydraulics_E2psiBelowground(
  E,
  hydraulicNetwork,
  psiIni = as.numeric(c(0)),
  ntrial = 10L,
  psiTol = 1e-04,
  ETol = 1e-04
)

hydraulics_E2psiAboveground(E, psiRootCrown, hydraulicNetwork)

hydraulics_E2psiFineRootLeaf(E, psiFineRoot, hydraulicNetwork)

hydraulics_E2psiNetworkStem1(
  E,
  hydraulicNetwork,
  psiIni = as.numeric(c(0)),
  ntrial = 10L,
  psiTol = 1e-04,
  ETol = 1e-04
)

hydraulics_E2psiNetwork(
  E,
  hydraulicNetwork,
  psiIni = as.numeric(c(0)),
  ntrial = 10L,
  psiTol = 1e-04,
  ETol = 1e-04
)

hydraulics_supplyFunctionOneXylem(
  psiSoil,
  v,
  kstemmax,
  stemc,
  stemd,
  psiCav = 0,
  maxNsteps = 200L,
  dE = 0.01
)

hydraulics_supplyFunctionTwoElements(
  Emax,
  psiSoil,
  krhizomax,
  kxylemmax,
  n,
  alpha,
  c,
  d,
  psiCav = 0,
  dE = 0.1,
  psiMax = -10
)

hydraulics_supplyFunctionThreeElements(
  Emax,
  psiSoil,
  krhizomax,
  kxylemmax,
  kleafmax,
  n,
  alpha,
  stemc,
  stemd,
  leafc,
  leafd,
  psiCav = 0,
  dE = 0.1,
  psiMax = -10
)

hydraulics_supplyFunctionBelowground(
  hydraulicNetwork,
  minFlow = 0,
  maxNsteps = 400L,
  ntrial = 10L,
  psiTol = 1e-04,
  ETol = 1e-04,
  pCrit = 0.001
)

hydraulics_supplyFunctionAboveground(
  Erootcrown,
  psiRootCrown,
  hydraulicNetwork
)

hydraulics_supplyFunctionFineRootLeaf(
  psiFineRoot,
  hydraulicNetwork,
  minFlow = 0,
  maxNsteps = 400L,
  ETol = 1e-04,
  pCrit = 0.001
)

hydraulics_supplyFunctionNetworkStem1(
  hydraulicNetwork,
  minFlow = 0,
  maxNsteps = 400L,
  ntrial = 200L,
  psiTol = 1e-04,
  ETol = 1e-04,
  pCrit = 0.001
)

hydraulics_supplyFunctionNetwork(
  hydraulicNetwork,
  minFlow = 0,
  maxNsteps = 400L,
  ntrial = 200L,
  psiTol = 1e-04,
  ETol = 1e-04,
  pCrit = 0.001
)

hydraulics_regulatedPsiXylem(E, psiUpstream, kxylemmax, c, d, psiStep = -0.01)

hydraulics_regulatedPsiTwoElements(
  Emax,
  psiSoil,
  krhizomax,
  kxylemmax,
  n,
  alpha,
  c,
  d,
  dE = 0.1,
  psiMax = -10
)

hydraulics_initSperryNetworks(x)

hydraulics_supplyFunctionPlot(
  x,
  draw = TRUE,
  type = "E",
  speciesNames = FALSE,
  ylim = NULL
)

Arguments

psiPlant

Plant water potential (in MPa).

psiUpstream

Water potential upstream (in MPa). In a one-component model corresponds to soil potential. In a two-component model corresponds to the potential inside the roots.

kxylemmax

Maximum xylem hydraulic conductance (defined as flow per leaf surface unit and per pressure drop).

c, d

Parameters of the Weibull function (generic xylem vulnerability curve).

allowNegativeFlux

A boolean to indicate wether negative flux (i.e. from plant to soil) is allowed.

psiCav

Minimum water potential (in MPa) experienced (for irreversible cavitation).

E

Flow per surface unit.

psiDownstream

Water potential upstream (in MPa).

psiRhizo

Soil water potential (in MPa) in the rhizosphere (root surface).

psiSoil

Soil water potential (in MPa). A scalar or a vector depending on the function.

krhizomax

Maximum rhizosphere hydraulic conductance (defined as flow per leaf surface unit and per pressure drop).

n, alpha, l

Parameters of the Van Genuchten function (rhizosphere vulnerability curve).

pCrit

Critical water potential (in MPa).

psi

Water potential (in MPa).

psiPrev

Water potential (in MPa) in the previous time step.

PLCprev

Previous proportion of loss conductance [0-1].

V

Capacity of the compartment per leaf area (in L/m2).

fapo

Apoplastic fraction (proportion) in the segment.

pi0

Full turgor osmotic potential (MPa).

eps

Bulk modulus of elasticity (MPa).

timestep

Time step in seconds.

psiStep

Water potential precision (in MPa).

psiMax

Minimum (maximum in absolute value) water potential to be considered (in MPa).

hydraulicNetwork

List with the hydraulic characteristics of nodes in the hydraulic network.

psiIni

Vector of initial water potential values (in MPa).

ntrial

Maximum number of steps in Newton-Raphson optimization.

psiTol

Precision for water potential estimates (in MPa).

ETol

Precision for water flow per surface unit.

psiRootCrown

Soil water potential (in MPa) at the root crown.

psiFineRoot

Water potential (in MPa) inside fine roots.

v

Proportion of fine roots within each soil layer.

kstemmax

Maximum stem xylem hydraulic conductance (defined as flow per leaf surface unit and per pressure drop).

stemc, stemd

Parameters of the Weibull function for stems (stem xylem vulnerability curve).

maxNsteps

Maximum number of steps in the construction of supply functions.

dE

Increment of flow per surface unit.

Emax

Maximum flow per surface unit.

kleafmax

Maximum leaf hydraulic conductance (defined as flow per leaf surface unit and per pressure drop).

leafc, leafd

Parameters of the Weibull function for leaves (leaf vulnerability curve).

minFlow

Minimum flow in supply function.

Erootcrown

Flow per surface unit at the root crown.

x

An object of class spwbInput.

draw

A flag to indicate whether the supply function should be drawn or just returned.

type

Plot type for hydraulics_supplyFunctionPlot, either "E", "ERhizo", "StemPsi", "RootPsi" or "dEdP").

speciesNames

A flag to indicate the use of species names instead of cohort names in plots.

ylim

Graphical parameter to override function defaults.

Details

Function hydraulics_supplyFunctionPlot draws a plot of the supply function for the given soil object and network properties of each plant cohort in x. Function hydraulics_vulnerabilityCurvePlot draws a plot of the vulnerability curves for the given soil object and network properties of each plant cohort in x.

Value

Values returned for each function are:

• hydraulics_E2psiXylem: The plant (leaf) water potential (in MPa) corresponding to the input flow, according to the xylem supply function and given an upstream (soil or root) water potential.

• hydraulics_E2psiVanGenuchten: The root water potential (in MPa) corresponding to the input flow, according to the rhizosphere supply function and given a soil water potential.

• hydraulics_E2psiTwoElements: The plant (leaf) water potential (in MPa) corresponding to the input flow, according to the rhizosphere and plant supply functions and given an input soil water potential.

• hydraulics_E2psiNetwork: The rhizosphere, root crown and plant (leaf water potential (in MPa) corresponding to the input flow, according to the vulnerability curves of rhizosphere, root and stem elements in a network.

• hydraulics_Ecrit: The critical flow according to the xylem supply function and given an input soil water potential.

• hydraulics_EVanGenuchten: The flow (integral of the vulnerability curve) according to the rhizosphere supply function and given an input drop in water potential (soil and rhizosphere).

• hydraulics_EXylem: The flow (integral of the vulnerability curve) according to the xylem supply function and given an input drop in water potential (rhizosphere and plant).

• hydraulics_supplyFunctionOneXylem, hydraulics_supplyFunctionTwoElements and hydraulics_supplyFunctionNetwork: A list with different numeric vectors with information of the two-element supply function:

  • E: Flow values (supply values).

  • FittedE: Fitted flow values (for hydraulics_supplyFunctionTwoElements).

  • Elayers: Flow values across the roots of each soil layer (only for hydraulics_supplyFunctionNetwork).

  • PsiRhizo: Water potential values at the root surface (only for hydraulics_supplyFunctionNetwork).

  • PsiRoot: Water potential values inside the root crown (not for hydraulics_supplyFunctionOneXylem).

  • PsiPlant: Water potential values at the canopy (leaf).

  • dEdP: Derivatives of the supply function.

• hydraulics_supplyFunctionPlot: If draw = FALSE a list with the result of calling hydraulics_supplyFunctionNetwork for each cohort.

• hydraulics_regulatedPsiXylem: Plant water potential after regulation (one-element loss function) given an input water potential.

• hydraulics_regulatedPsiTwoElements: Plant water potential after regulation (two-element loss function) given an input soil water potential.

Author(s)

Miquel De Cáceres Ainsa, CREAF

References

Sperry, J. S., F. R. Adler, G. S. Campbell, and J. P. Comstock. 1998. Limitation of plant water use by rhizosphere and xylem conductance: results from a model. Plant, Cell and Environment 21:347–359.

Sperry, J. S., and D. M. Love. 2015. What plant hydraulics can tell us about responses to climate-change droughts. New Phytologist 207:14–27.

See Also

hydraulics_psi2K, hydraulics_maximumStemHydraulicConductance, spwb, soil

Examples

kstemmax = 4 # in mmol·m-2·s-1·MPa-1
stemc = 3 
stemd = -4 # in MPa
psiVec = seq(-0.1, -7.0, by =-0.01)

#Vulnerability curve
kstem = unlist(lapply(psiVec, hydraulics_xylemConductance, kstemmax, stemc, stemd))
plot(-psiVec, kstem, type="l",ylab="Xylem conductance (mmol·m-2·s-1·MPa-1)", 
     xlab="Canopy pressure (-MPa)", lwd=1.5,ylim=c(0,kstemmax))